SHS2 Additional Mathematics · Semester 2 Week 18: Making Predictions with Data

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.1 - Describe the number of ways objects can be arranged using fundamental counting principles.

By the end of the lesson, learners can:

State the fundamental counting principle in their own words and explain when to apply it.
Use the fundamental counting principle to determine the total number of outcomes when two or more independent choices are made.
Apply the multiplication rule to solve problems involving arrangements where items are selected from a given set without repetition.
Construct simple counting problems, such as those used for elections, registrations, or codes, and solve them using the fundamental counting principle.
Communicate their reasoning clearly, using appropriate mathematical vocabulary such as “outcome”, “arrangement”, “choice”, and “independent events”, when working in pairs or groups.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Making Predictions with Data (4.2)
Content standard: 2.4.2.CS.2 - Apply the concepts of permutation and combination to solve real life problems. 2.4.2.LO.1 Solve problems using the axioms and the laws of probability. 2.4.2.LO.2 Solve real life problems using combination and permutation.
Indicator: 2.4.2.LI.1 - Describe the number of ways objects can be arranged using fundamental counting principles.
Suggested placement: Semester 2, Week 18 (Week 38 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.426: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 426

Exemplars (from the NaCCA curriculum)

Group work, Talk for Learning, and Building on what others say.
Learning Experience: Learners in groups create problems using the axioms and laws of probability.
Activity 1: Fundamental counting principles Learners in pairs recollect the fundamental counting techniques and principles for the outcomes of some experiments and state the number of ways each can be performed.
Example 1: If a sports club decides to elect a chairman and a secretary from 5 members, assuming the same person cannot hold both positions, find the number of ways this can be done.
Solution: Thus, number of ways of choosing a chairman = 5 And the number of ways to choose a secretary = 4 =5×4 = 20
Example 2: The Department of Vehicle and Licensing Authority designs the registration of each car with 2 letters from 𝐸, 𝑅, 𝐺, 𝑇 and 3 digits from 1,4,5,6 on a given day. How many cars can be registered on that day under this arrangement? Solution: Firstly, how many 2-letter arrangements can be formed from the 4 letters, 𝐸, 𝑅, 𝐺, 𝑇? ,! This is 4𝑃 ) = (,*))!
4! = = 12 2! Similarly, arranging 3 digits from the digits 1,4,5,6 is 4𝑃 "
4! 4𝑃 " = (4 − 3)! 4! = 1! = 24
Teaching and Learning Resources:
- Real-life data samples from both the school community and/or outside the school community.
- ICT tools
- YEAR THREE
Assessment (2.4.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.